In wireless communication systems, small differences between frequency of a transmitted signal's carrier frequency and the receiver's locally generated carrier frequency will effect the accuracy of the received signal, and should therefore be corrected. These frequency offsets are typically caused by inaccuracies in the receiver's phase lock loop tracking the received signal's carrier frequency, as well as temperature variations in local oscillators. If these frequency offsets are not corrected, phase errors in the estimation of data symbols will occur, which degrades performance.
An increasingly important wireless technology is orthogonal frequency division multiplexing (OFDM) which is robust in noisy and rapidly changing environments, such as those in which WLAN's are employed. OFDM systems transmit on a number of sub-carriers (having different carrier frequencies) simultaneously, such that a series of symbols are sent over different sub-carriers in the form of a packet.
In OFDM systems, the packet preamble allows coarse and fine carrier frequency offset estimates to be made in order to adjust the receiver oscillator signals and phase lock loop tracking to correctly receive a signal from a transmitter having a slightly different carrier frequency. This is described for example in Liu, Li, Stoica,“A MIMO system with backwards compatibility for OFDM based WLANs”, SPAWC 2003, 15-18 Jun. 2003, pages 130-134.
Once this initial estimate is known, tracking of the frequency offset can also be carried out over the duration of the packet in order to account for changes in channel conditions and other effects which can influence the received carrier frequency. Pilot symbols, ie symbols known to the receiver, are inserted among the data symbols of the packet to facilitate tracking of the carrier frequency. Various ways of achieving this are known.
For example in IEEE802.11a, an OFDM based WLAN standard, 4 subcarriers are allocated for dedicated pilot symbols, which are used for tracking frequency offsets. Between two consecutive OFDM symbols, a frequency offset will manifest itself as a phase rotation on each subcarrier. By measuring this phase difference for each pilot subcarrier, the frequency offset can be estimated (since the channel is assumed to be constant and the transmitted symbols are known, any phase change is due to a frequency offset).
The frequency offset on each subcarrier is typically caused by a combination of an error in the receiver generated carrier frequency which is used for tracking the received signal in a phase lock loop (PLL), and an error in the sampling clock. The former will cause a constant frequency shift on all subcarriers, while the latter will be proportionally worse towards the band edges. In IEEE802.11a, the 4 pilots are used on subcarriers −21, −7, +7, and +21 (out of 64 subcarriers spanning 20 MHz, the subcarriers are numbered −32 to +31). Once the frequency shift on each subcarrier has been estimated, the following system of equations is obtained:Δf−21=−21α+βΔf−7=−7α+βΔf7=7α+βΔf21=21α+βwhere α is the sampling clock offset and β is the carrier generated carrier frequency offset.
As is known, a least squares line fit can be performed to obtain a best estimate for the two offsets, and this leads to the following estimates for the two offset components:
            α      ^        =                                        -            3                    ⁢          Δ          ⁢                                          ⁢                      f                          -              21                                      -                  Δ          ⁢                                          ⁢                      f                          -              7                                      +                  Δ          ⁢                                          ⁢                      f            7                          +                  3          ⁢          Δ          ⁢                                          ⁢                      f            21                              140                  β      ^        =                            Δ          ⁢                                          ⁢                      f                          -              21                                      -                  Δ          ⁢                                          ⁢                      f                          -              7                                      +                  Δ          ⁢                                          ⁢                      f            7                          +                  Δ          ⁢                                          ⁢                      f            21                              4      
Another method of achieving frequency offset estimates is described in V. S. Abhayawardhana, I. J. Wassell, “Residual frequency offset correction for coherently modulated OFDM systems in wireless communication”, Vehicular Technology Conference, 6-9 May 2002, vol 2, Pages 777-781. This describes tracking of frequency offsets by using decision feedback. An estimate of the channel response H is made for each sub-carrier based on a decoded training symbol from each respective sub-carrier. A subset of these subcarriers is then selected which has a channel response above a certain threshold. A maximum likelihood estimate of the residual frequency estimate is then obtained using only these sub-carriers.
Multiple Input Multiple Output (MIMO) arrangements are being increasingly investigated as a way of increasing the data rate of existing wireless systems. For example the developing WLAN standard IEEE802.11n is expected to use MIMO technology. MIMO involves using multiple antennas at the transmitter which simultaneously transmit different symbols, which in turn are received at a receiver with multiple receiver antennas. Special processing in the transmitter and receiver is required in order for the receiver to be able to recover the transmitted symbols using the various combinations of received symbols from its different receiving antennas.
MIMO systems are inherently multi-path signal propagation systems which adds a further layer of complexity to the task of estimating the frequency offset between the transmitter and receiver. An example of frequency offset tracking estimation in a MIMO system is described in Oberli, Daneshrad, “Maximum Likelihood Tracking Algorithms for MIMO-OFDM”, IEEE Communications Society 2004, vol 4, p 2468-2472, June 2004. However this arrangement is complex and requires knowledge of the channel and therefore makes it susceptible to channel estimation errors.
Therefore there is a need for an improved frequency offset tracking method and apparatus especially for MIMO systems.